Unit of Instruction
Brian Roska
EdTech 506-4172
Dr. Yu-Chang Hsu
Summer 2012
Subject Area: Mathematics
Grade Level: 6th Grade
Unit Name: Factors and Multiples
Unit Goals:
Understanding the number system and its patterns are an important part of developing fluent
mathematic skills. Specifically, students need to be able to multiply and divide numbers efficiently and
accurately. These problems often time require breaking a whole number down into equal-size pieces or
finding a number into which a given number will divide equally. Solving problems such as these involves
finding factors and multiples.
The goal of this unit is for each student to prove he/she can:
 Develop understanding of factors and multiples and the relationships between them.
 Visualize and represent a factor pair as the dimensions of a rectangle.
 Classify numbers by their characteristics using Venn diagrams as a tool for sorting and
classifying.
 Develop understanding of common factors and common multiples, and the relationships among
them.
 Observe regularity or patterns in common factors of numbers to reason about and predict
future occurrences and solve problems.
 Develop strategies for finding the greatest common factor.
 Observe regularity or patterns in common multiples of numbers to reason about and predict
future occurrences and solve problems.
 Develop strategies for finding the least common multiple.
 Use the multiplicative structure of numbers, such as primes, composites, factors, multiples, and
square numbers, to reason mathematically and to solve interesting problems.
Core Standards:
This unit covers the following Number System Standards for 6th grade as set forth by the Common Core
State Standards for Mathematics:
Compute fluently with multi-digit numbers and find common factors and multiples.
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6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and
the least common multiple of two whole numbers less than or equal to 12. Use the distributive
property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a
sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Taken from the Common Core State Standards Initiative at http://www.corestandards.org/thestandards/mathematics/grade-6/the-number-system/
Student Characteristics:
Students involved with learning this lesson will be 6th graders in a general classroom setting. The school
is set in a fairly rural area with approximate student ethnic ratios: 81% Caucasian, 12% Black, 4%
Hispanic-Non White and 3% Asian. This is also the only middle school in the district and most of the
students have been together since elementary school. Appropriate interventions will be given to
students who have requirements based on IEP, 504 etc.
Student Present Level of Knowledge:
Students completing this unit should have successfully completed the 5th grade math program and
should have basic multiplication and division skills.
Classroom Layout:
The classroom layout will change frequently as the students are asked to work both independently and
in small groups. Much of the activities and discussion during this unit is done amongst peers and the
students will be in groups of three or four during these work periods.
Unit Introduction:
The unit will be introduced using a discussion of how we use numbers and what we plan on doing with
numbers in this unit. Several interesting questions will be posed that do not need to be answered at this
time. Here is an example question. Allen is standing on a train platform watching trains come in and out
of the station. The train on track A comes into the station every 5 minutes and the train on track B
arrives every 6 minutes. If the two trains are there together now, how many minutes will it before Allen
sees two trains arrive at the same time again? These questions are to create excitement and to show
the students what they will be able to complete later in the unit. Next, discuss the unit goals with the
students in order to create expectations for the type of work they will be doing and the ideas they will
be learning.
Materials and Resources:
 Calculators
 Paper Clips
 Colored chips (12 of 2 different colors per pair of students)
 Colored pens, markers or pencils
 Square tiles
 Grid paper
 Scissors
 Tape or glue
 Handouts of product game boards
 Interactive whiteboard or overhead projector w/ transparencies and markers
 Pencils
 Student journal or notebook
Visuals Implemented:
1. Banner Graphic – created as a header for all web pages
2. Unit Goals – to show what the students will learn
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Factor Rainbow – used to show factor pairs
Factor Tree – to show how a number can be broken into prime factors
Product Game and Instructions – a game and instructions made to show how to play
Factor Rectangles – made to show how to represent factors graphically
GCF Venn Diagram – shows relationships between factors of numbers
GCF Factor Groups – shows a graphical relationship between factors of numbers
LCM Ferris Wheels – shows relationships between multiples of numbers
Assessment/ Evaluation:
Assessments will be a mixture of informal and formal measurements. Students will be informally
observed throughout the course of the unit and each lesson assignment is also graded on a 4 point
rubric. Students will be required to take various quizzes and a Unit Test. After the Unit Test each
students will need to complete a self assessment regarding their unit performance. The ongoing and
final assessments will show that the student has attained the outcomes of the lesson as stated in the
goals.
* Adapted from Unit Plan at http://edtech.tennessee.edu/~bobannon/unit_plans.html